This article is cited in 4 papers

Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source

M. O. Korpusov<sup>ab

a</sup> Lomonosov Moscow State University
^b Peoples' Friendship University of Russia, Moscow

Abstract: We consider an abstract Cauchy problem with non-linear operator coefficients and prove the existence of a unique non-extendable classical solution. Under certain sufficient close-to-necessary conditions, we obtain finite-time blow-up conditions and upper and lower bounds for the blow-up time. Moreover, under certain sufficient close-to-necessary conditions, we obtain a result on the existence of a global-in-time solution independently of the size of the initial functions.

Keywords: non-linear Sobolev-type equations, blow-up, local solubility, non-linear capacity, bounds for the blow-up time.

UDC: 517.538

MSC: 35B44, 35L15, 35L71, 35L90

Received: 05.11.2018
Revised: 19.03.2019

DOI: 10.4213/im8880

 English version: Izvestiya: Mathematics, 2020, 84:5, 930–959

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